The protractor is an ancient instrument. In its simplest form, it is a semi-circular disk with angles ranging from zero to 180 degrees around its circumference. Such a device is known to have been used by the 13th century as incorporated into a device, known as a torquetum, which was used in astronomical observations.
Every protractor since the year 1200 has measured angles. Many protractors not only measure angles, but also achieve some other function, such as assisting artisans in laying out angles, providing convenient means for drawing angles, dividing angles, and so on.
The National Assessment of Educational Progress in the United States in 1993 reported that only one third of eighth graders using conventional protractors could successfully measure a 127 degree angle, and that was with an allowance of three degrees on either side of 127 degrees. Any answer between 124 and 130 degrees was counted as correct. Typically, a teacher of fifth or sixth graders might spend an entire class period teaching how to use the protractor, with the result that about half the class can correctly measure an angle. After another class period of teaching, another quarter of the class may have reached proficiency, leaving a quarter of the class without an understanding of how to use the standard protractor. By test time, only a third of the students can measure an angle. Some teachers devote three or four class periods trying to teach students how to measure angles using a conventional protractor.
The use of conventional protractors has been accompanied by ambiguity that reduces student comprehension. Every ambiguity in a protractor requires the student to learn a rule to resolve the ambiguity. Later, at test time, the student has to recall and apply the rule correctly. By eliminating the ambiguity in angle measurement, the student learns faster and achieves greater proficiency.
For example, in the conventional half moon protractor, there are two scales, one reading left to right and the other right to left. For every angle measured, there is a correct and incorrect answer. That is a major ambiguity for students. Another ambiguity is where to line up the legs of the angle. There are several possibilities, which creates more ambiguity. The same can be said for all protractors known prior to the present invention.
To avoid the ambiguities just noted, a pivoted protractor may be used. However, if the pivot is located anywhere other than in line with the two measuring edges, it will scissor, meaning the vertex of the enclosed angle will travel outward as smaller angles are created.
Another problem with conventional protractors is that many angles, both those drawn by students and those in books, have legs too short to reach to the curved portion of the conventional protractor. The angle is unreadable without the awkward and inconvenient step of extending the legs with a ruler and pencil, possibly into the text of the school book. Using a small protractor is no solution, because small degree markings are unreadable.
Finally, the process for constructing angles using a standard half moon is tedious. It involves making several tick marks, removing the protractor from the paper, and then connecting the tick marks.
The object of the present invention is to improve the speed with which students learn to measure and draw angles. The utility of the invention is not only that it successfully measures angles, but also that children can master angle measurement faster and better using the present invention.